A rare manuscript with notes made by Albert Einstein was auctioned for more than $13 million.
They contain the early calculations that eventually became Einstein's general theory of relativity.
Auction house Christie's sold it in Paris to an unnamed buyer.
Notes and calculations made by Albert Einstein sold for more than $13 million at an auction in Paris.
Auction house Christie's had predicted the manuscript would sell for between $2.25m and $3.38m.
"This is without a doubt the most valuable Einstein manuscript ever to come to auction," Christie's said in a statement before the sale, this week.
The identity of the buyer has not been revealed.
The 54-page document, which Einstein co-authored with his friend and colleague Michele Besso, is one of just two papers that show the theoretical physicist's early workings on his seminal theory of relativity.
The theory, published in 1915, is still considered one of the most important ideas in modern physics.
"Einstein is someone who kept very few notes, so the mere fact that the manuscript survived and made its way to us already makes it absolutely extraordinary," Vincent Belloy, an expert at Christie's said in a statement.
Belloy praised Michele Besso for having had the foresight to save the pages.
The documents feature notes made by Einstein and Besso by hand between 1913 and 1914, mostly in black ink.
Christie's said that 26 of the pages had been written by Einstein, 25 were written by Besso and three contain notes made by both.
"The manuscript isn't bound, and there are many different types of loose paper, so you get the impression of a working document that's full of energy, as if both men would grab the first page they could find to scribble their findings on," Belloy said.
The papers show the scientist making the initial calculations that would form the foundation for his theory, but making some mistakes along the way.
"Einstein makes errors in this manuscript, and that I think makes it even greater in a way, because we see the persistence, the thought that was in the process of being built, that is being corrected and redirected," Belloy said.
Experts said that the manuscript showed that the theory was the culmination of years of work.
Belloy added that the manuscript also revealed the different working styles of the two men.
"What's interesting is the sense of personality that comes across in these pages," he said.
"You get the impression that Einstein was perhaps more confident in his calculations since his sheets are much lighter in terms of textual content and reserved almost exclusively for calculations. Besso, by contrast, often added written notes in the margin."
The document has become the most valuable of Einstein's notes ever to be sold. In May, a handwritten letter by the scientist containing his E=mc² equation sold for more than $1.2m.